Topologically protected Grover's oracle for the partition problem
The number partitioning problem (NPP) is one of the NP-complete (nondeterministic polynomial-time complete) computational problems. Its definite exact solution generally requires a check of all $$N$$ solution candidates, which is exponentially large. Here we describe a path to the fast solution of this problem in $$\sqrt{N}$$ quasi-adiabatic quantum annealing steps. We argue that the errors due to the finite duration of the quantum annealing can be suppressed if the annealing time scales with $$N$$ only logarithmically. Moreover, our adiabatic oracle is topologically protected, in the sense that it is robust against small uncertainty and slow time dependence of the physical parameters or the choice of the annealing protocol. In conclusion, we also argue that our approach can solve many other famous NP-complete computational problems in $$\sqrt{N}$$ steps.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1997183
- Report Number(s):
- LA-UR-23-24130
- Journal Information:
- Physical Review A, Journal Name: Physical Review A Journal Issue: 2 Vol. 108; ISSN 2469-9926
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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